Calculating $E[exp(\int_0^T W_s dW_s)]$?

Question

By using Ito's Formula I was able to calculate $\int_0^T W_t dW_t = \frac {W^2_T} 2 - \frac T 2$, after this how to proceed in order to calculate Expected value , I know that: $$E[X] = \int_{-\infty}^{\infty} exp⁡(X)f(x)dx$$